Elastic tailoring of particulate composites via an auxetic spherical interphase and particle-size distribution effects

Auxetic solids with negative Poisson’s ratio have been widely discussed for enhanced indentation and energy absorption, yet their possible use as effective engineered interphases in particulate structural composites remains comparatively underexplored. This study considers a three-phase isotropic composite in which rigid spherical particles are surrounded by a thin auxetic interphase of fixed thickness and embedded in a conventional matrix. The formulation is based on classical coated-sphere equivalence and Mori–Tanaka averaging, but focuses on two specific modeling features: a negative-Poisson’s-ratio interphase and a lognormal distribution of particle core radii while the coating thickness is kept fixed for all particles. Under this fixed-thickness assumption, the core-to-coating volume ratio becomes radius-dependent, leading to a geometric size-partition effect within linear elasticity. Each coated particle is first replaced by an equivalent homogeneous inclusion, and the macroscopic response is then estimated using Mori–Tanaka homogenization. The particle-size distribution is incorporated to quantify how shifts in the median radius modify the effective moduli while keeping the overall coated-particle volume fraction constant. Phase-averaged localization indicators are further used to examine hydrostatic and deviatoric matrix amplification trends. The results show modest but systematic changes in effective stiffness, Poisson’s ratio, and bulk–shear balance over the investigated parameter ranges. The model is intended as a computationally light screening tool for interphase-property, coating-thickness, and particle-size-distribution studies in coated particulate composites.